Iovine’s company is currently working on a service called Project Daisy; Beats acquired streaming music service MOG last July, a move seen as an attempt to augment Beats’ line of headphones and speakers developed by Iovine and rap legend Dr. Dre.

Reuters quotes three anonymous sources as saying the meeting was “informational” but the article adds that Apple “has been widely reported to be considering a music-streaming service to complement iTunes, the largest repository of music for sale.”

If Apple were to launch a streaming music service, it certainly wouldn’t be the first to do so, but the company’s enormous base of iTunes users and iTunes’ tight integration with Apple’s hardware products would likely help such a service quickly scale to compete with the likes of Spotify and similar competitors.

This next bit is pure speculation on my part, so please indulge me. I see a couple of possible scenarios here:

If Apple were to launch its own streaming music service that exclusively leveraged whatever Beats is working on, and assuming the service would be priced like other services, we might expect to see a $5-per-month option that featured the ability to stream music to the iTunes desktop software, and a $10-per-month option that featured the ability to download tracks for offline listening and for use on mobile devices. I’d be surprised to see the ability to stream or download tracks to anything other than iTunes or Apple hardware products, however, with the exception of Windows PCs that run the iTunes software. I wouldn’t expect that you’d be able to use this service with non-Apple mobile devices, in other words, and people want to listen to their music while in places other than in front of their computers, believe it or not. Though Apple has a large base of iPhone, iPod and iPad owners, this tactic would still limit the service’s reach.

However, the idea of Apple partnering with Beats on this service makes more sense. Beats would do most or all of the heavy lifting, while Apple could integrate the service with iTunes and Apple hardware devices. Beats, however, would be able to offer the Daisy app or whatever it’d be called on Android phones and other mobile platforms as well. Beats already has partnerships with HTC, which makes Android and Windows Phone hardware, and HP, which makes computers and just recently started making Android hardware.

As Reuters points out, Iovine “has a long association with Apple and was one of the first music industry executives to sign onto what was then Apple’s nascent iTunes initiative, announced in 2001.” He also told All Things D that he tried to sell Steve Jobs on the idea of a subscription music service in 2003. But the fact that his company now has partnerships with Apple competitors makes the idea of an Apple-exclusive streaming music service seem unlikely. A Beats-branded music service that hooks into iTunes while still playing nicely with others might be the most palatable scenario for everyone involved.

We’ll see where this goes, if anywhere, though. It feels like we’ve been collectively asking about all-you-can-eat iTunes subscriptions for the better part of a decade now.